The English attacking midfielder scored twice and provided an assist for Joao Pedro in a devastating display in the revamped tournament's decider that left the European and French champions, who finished with 10 men, shell-shocked.
Chelsea, who won the 2021 Club World Cup in its previous format, struck first in the 22nd minute when PSG fullback Nuno Mendes gifted possession to Malo Gusto.
While his initial effort was blocked by Mendes, Gusto collected the rebound and found Palmer unmarked in the middle and the midfielder made no mistake, slotting a tidy finish just inside the left post.
Palmer doubled the lead after the 30th-minute cooling break with a goal of sublime quality. Latching onto a precise through ball from Levi Colwill, he cut inside before faking a pass to dummy a defender and firing into the bottom-left corner.
Palmer then turned provider, running up the channel before finding Joao Pedro, who took the ball in his stride and beat the offside trap before chipping his finish beautifully over keeper Gianluigi Donnarumma.
PSG's misery was completed when Joao Neves was sent off for pulling Marc Cucurella's hair in the 83rd minute, as PSG's players grew in frustration as the match progressed.
The encounter turned into an ill-tempered match at the end, with players going at each other after the final whistle, but the flare-ups quickly dissipated as Chelsea's players went to celebrate with their fans.
"It's a great feeling. Even better because everyone doubted us before the game, we knew that. To put a fight on like we did, it's good," Palmer told DAZN.
"The gaffer put a great gameplan out. He knew where the space was going to be. He tried to free me up as much as possible and I just had to repay him and score some goals."
Chelsea arrived in the U.S. after winning Europe's third-tier Conference League and on the back of a domestic campaign in which they just managed a top-four Premier League finish.
Prior to the match, Chelsea manager Enzo Maresca said he was expecting a "game of chess" against PSG coach Luis Enrique, but it was a quick checkmate for the Italian who gave a tactical masterclass.
Maresca's team employed a relentless high press and emulated the tactics used by Brazilian outfit Botafogo, who had beaten PSG 1-0 in the group stage and were the only team to score against Luis Enrique's side in the previous eight games.
Their press caused PSG all sorts of trouble and when Maresca's side couldn't regain possession, they sat deep, frustrating the European champions, who were unable to play their usual game.
The direct and pacey football we had become used to seeing from PSG was Chelsea's game on Sunday, with Palmer, Gusto and Joao Pedro picking apart the PSG defence, especially on the left side.
Other than an early golden opportunity for PSG's Desire Doue that was wasted, the first half was all Chelsea's and, after they opened their three-goal lead, the French side could never recover.
